The line common to the given families of line `a(x+y` `+1)+b(2x-3y-8)=0` and `lambda(x-y-1)+mu(2x-y` `-1)=0` is

The equation of straight line belonging to both the families of lines (x-y+1)+lambda_1(2x-y-2)=0 and (5x+3y-2)+lambda_2(3x-y-4)=0 where lambda_1, lambda_2 are arbitrary numbers is (A) 5x -2y -7=0 (B) 2x+ 5y - 7= 0 (C) 5x + 2y -7 =0 (D) 2x- 5y- 7= 0

If it is possible to draw a line which belongs to all the given family of lines y-2x+1+lambda_1(2y-x-1)=0,3y-x-6+lambda_2(y-3x+6)=0 , a x+y-2+lambda_3(6x+a y-a)=0 , then (a) a=4 (b) a=3 (c) a=-2 (d) a=2

Consider the family of lines 5x+3y-2+lambda_(1)(3x-y-4)=0 " and " x-y+1+lambda_(2)(2x-y-2)=0 . Find the equation of a straight line that belongs to both the families.

Consider the family of line (x+y-1)+lamda(2x+3y-5)=0 and (3x+2y-4)+mu(x+2y-6)=0 Equation of a straight line that belongs to both the families is:

The mid-point of the line joining the common points of the line 2x-3y+8=0" and "y^(2)=8x, is

The value of the lambda if the lines (2x+3y+4)+lambda(6x-y+12)=0 are

If the pairs of lines x^2+2x y+a y^2=0 and a x^2+2x y+y^2=0 have exactly one line in common, then the joint equation of the other two lines is given by (1) 3x^2+8x y-3y^2=0 (2) 3x^2+10 x y+3y^2=0 (3) y^2+2x y-3x^2=0 (4) x^2+2x y-3y^2=0

If a circle passes through the points of intersection of the lines 2x-y +1=0 and x+lambda y -3=0 with the axes of reference then the value of lambda is :

Find the angle between the lines x+3y-8=0 and 2x-3y+6=0 .

If the straight line x/a+y/b=1 passes through the line point of intersection of the lines x+y=3 and 2x-3y=1 and is parallel to x-y-6=0 , find a and b.